Building a referral engine, on purpose
Most shops have happy customers. Most shops don't ask them to send anyone.
Ask at the peak moment
The right time to ask is right after the work is finished and the customer is visibly happy, not in a follow-up email a week later. Train whoever closes out the job to ask, on script if needed.
Make it stupid easy to send a friend
A pre-written text the customer can forward beats a referral card every time. 'Hey, you used [shop] for [thing]? Here's their number.' That's the entire mechanism.
Reward both sides
A discount or credit for both the referrer and the new customer outperforms one-sided rewards by a wide margin. The cost is trivial compared to the lifetime value of the referred customer.
Take your version of this question further
This is one operator-tested angle on the question. Your shop, your size, your trade, and your team change the answer. Ask your specific version inside Ask a Shop Owner to get a response grounded in how owners like you actually handled it.